MinT - Best Known (187−84, 187, s)-Nets in Base 3

Best Known (187−84, 187, s)-Nets in Base 3

(187−84, 187, 80)-Net over F₃ — Constructive and digital

Digital (103, 187, 80)-net over F₃, using

3 times m-reduction [i] based on digital (103, 190, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 95, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(187−84, 187, 127)-Net over F₃ — Digital

Digital (103, 187, 127)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−84, 187, 1058)-Net in Base 3 — Upper bound on s

There is no (103, 187, 1059)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 170509 943550 797151 493768 784183 295167 309988 862874 763208 752804 625047 017513 891865 333898 824789 > 3¹⁸⁷ [i]